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A bond manager has a $10 million portfolio with a duration of 4 years which he would like to hedge against interest rate risk for

A bond manager has a $10 million portfolio with a duration of 4 years which he would like to hedge against interest rate risk for a short period. There is a bond futures contract with a per unit futures price of $97.50, and each contract is for delivery of 1,000 units. The cheapest to deliver bond covered by the contract has a duration of 3.4 years. What contract position should the manager take to hedge interest rate risk? Given an exact answer (do not round to an integer number of contracts) and state whether the position is short or long.

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